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<div><span class="kw">theorem </span><a NAME="T65"><span class="comment"><font color="firebrick">:: SF_MASTR:65</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">I</font> being   <a href="compos_1.html#NM4" title="COMPOS_1:NM.4">Program</a> of <br/>  for <font color="Olive" title="b2">n</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><br/>  for <font color="Olive" title="b3">s</font>, <font color="Olive" title="b4">t</font> being   <a href="memstr_0.html#NM2" title="MEMSTR_0:NM.2">State</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a><br/>  for <font color="Olive" title="b5">P</font>, <font color="Olive" title="b6">Q</font> being   <a href="compos_1.html#NM2" title="COMPOS_1:NM.2">Instruction-Sequence</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>  st <font color="Olive" title="b1">I</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b5">P</font> &amp; <font color="Olive" title="b1">I</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b6">Q</font> &amp;  <a href="memstr_0.html#K7" title="MEMSTR_0:func.7">Start-At</a> (<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b3">s</font> &amp;  <a href="memstr_0.html#K7" title="MEMSTR_0:func.7">Start-At</a> (<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b4">t</font> &amp; <font color="Olive" title="b3">s</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">|</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K3" title="SF_MASTR:func.3">UsedILoc</a> <font color="Olive" title="b1">I</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">t</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">|</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K3" title="SF_MASTR:func.3">UsedILoc</a> <font color="Olive" title="b1">I</font></span>)</span> &amp; <font color="Olive" title="b3">s</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">|</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K6" title="SF_MASTR:func.6">UsedI*Loc</a> <font color="Olive" title="b1">I</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">t</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">|</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K6" title="SF_MASTR:func.6">UsedI*Loc</a> <font color="Olive" title="b1">I</font></span>)</span> &amp; (  for <font color="Olive" title="b7">m</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st <font color="Olive" title="b7">m</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Olive" title="b2">n</font> holds <br/> <a href="memstr_0.html#K5" title="MEMSTR_0:func.5">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Olive" title="b5">P</font>,<font color="Olive" title="b3">s</font>,<font color="Olive" title="b7">m</font>)</span>)</span> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Olive" title="b1">I</font> ) holds <br/>( (  for <font color="Olive" title="b7">m</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st <font color="Olive" title="b7">m</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Olive" title="b2">n</font> holds <br/> <a href="memstr_0.html#K5" title="MEMSTR_0:func.5">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Olive" title="b6">Q</font>,<font color="Olive" title="b4">t</font>,<font color="Olive" title="b7">m</font>)</span>)</span> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Olive" title="b1">I</font> ) &amp; (  for <font color="Olive" title="b7">m</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st <font color="Olive" title="b7">m</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b2">n</font> holds <br/>(  <a href="memstr_0.html#K5" title="MEMSTR_0:func.5">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Olive" title="b5">P</font>,<font color="Olive" title="b3">s</font>,<font color="Olive" title="b7">m</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="memstr_0.html#K5" title="MEMSTR_0:func.5">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Olive" title="b6">Q</font>,<font color="Olive" title="b4">t</font>,<font color="Olive" title="b7">m</font>)</span>)</span> &amp; (  for <font color="Olive" title="b8">a</font> being   <a href="scmfsa_2.html#NM1" title="SCMFSA_2:NM.1">Int-Location</a>  st <font color="Olive" title="b8">a</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="sf_mastr.html#K3" title="SF_MASTR:func.3">UsedILoc</a> <font color="Olive" title="b1">I</font> holds <br/><span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Olive" title="b5">P</font>,<font color="Olive" title="b3">s</font>,<font color="Olive" title="b7">m</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b8">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Olive" title="b6">Q</font>,<font color="Olive" title="b4">t</font>,<font color="Olive" title="b7">m</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b8">a</font> ) &amp; (  for <font color="Olive" title="b8">f</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">FinSeq-Location</a>   st <font color="Olive" title="b8">f</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="sf_mastr.html#K6" title="SF_MASTR:func.6">UsedI*Loc</a> <font color="Olive" title="b1">I</font> holds <br/><span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Olive" title="b5">P</font>,<font color="Olive" title="b3">s</font>,<font color="Olive" title="b7">m</font>)</span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Olive" title="b8">f</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Olive" title="b6">Q</font>,<font color="Olive" title="b4">t</font>,<font color="Olive" title="b7">m</font>)</span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Olive" title="b8">f</font> ) ) ) )</div></div>
